GEOPHYSICAL RESEARCH LETTERS, VOL. 36, L14807, doi:10.1029/2009GL038507, 2009
Heating and cooling of the thermosphere by internal gravity waves
Erdal Yiğit1,2,3 and Alexander S. Medvedev2
Received 3 April 2009; revised 10 June 2009; accepted 17 June 2009; published 21 July 2009.
[1] For the first time, estimates of heating and cooling in the
upper thermosphere due to dissipating and breaking gravity
waves (GWs) of tropospheric origin have been obtained with
a comprehensive general circulation model (GCM). A GW
parameterization specifically designed for thermospheric
heights has been implemented in the CMAT2 GCM covering
altitudes from the tropopause to the F2 region, and
simulations for the June solstice have been performed.
They reveal that the net thermal effect of GWs above the
turbopause is cooling. The largest (up to 170 K d1 in a
zonally and temporally averaged sense) cooling takes place
in the high latitudes of both hemispheres near 210 km. The
instantaneous values of heating and cooling rates are highly
variable, and reach up to 500 and 3000 K d1 in the F2
region, respectively. Inclusion of the GW thermal effects
reduces the simulated model temperatures by up to 200 K
over the summer pole and by 100 to 170 K at other latitudes
near 210 km. Citation: Yiğit, E., and A. S. Medvedev (2009),
2007], systematic estimates have not been attempted at
these heights, to the best of our knowledge. Among possible
reasons for this deficiency are that thermosphere GCMs
either do not couple the troposphere with the upper atmosphere, or they lack appropriate GW parameterizations that
can realistically account for wave dissipation above the
turbopause. Recently, we have developed a suitable spectral
GW scheme [Yiğit et al., 2008] and implemented it in the
Coupled Middle Atmosphere-Thermosphere-2 (CMAT2)
GCM [Yiğit et al., 2009]. It has been shown that dynamical
effects of GWs propagating from below are not only nonnegligible in the TI, but are comparable with those of ion
friction, at least below 180 – 200 km. In this paper, we
turn our attention to thermal effects of dissipating internal
GWs of lower atmospheric origin, estimate them, and assess
their role in the TI. This is done with numerical experiments employing the CMAT2 GCM and the spectral GW
parameterization.
Heating and cooling of the thermosphere by internal gravity waves,
Geophys. Res. Lett., 36, L14807, doi:10.1029/2009GL038507.
2. Model Description
1. Introduction
[2] Dissipating and/or breaking gravity waves (GWs)
produce heating of the mean flow [Gavrilov, 1990; Becker
and Schmitz, 2002; Medvedev and Klaassen, 2003], and
induce a downward sensible heat flux [Walterscheid, 1981;
Medvedev and Klaassen, 2003]. The former effect is the
result of irreversible conversion of mechanical wave energy
into heat. The latter arises due to altering the phase relationship between wave fluctuations of temperature and vertical
velocity by the diffusivity associated with GW dissipation/
breaking. Thermal effects of internal GWs generated in the
troposphere have been studied in the mesosphere-lower
thermosphere (MLT) using comprehensive general circulation models (GCMs) [Medvedev and Klaassen, 2003;
Becker, 2004]. It was found that during solstices, GWs can
produce monthly mean cooling rates up to several K d1 in
the lower thermosphere and a somewhat weaker heating
below. These values are comparable with radiative heating/
cooling rates, and should not be neglected in the MLT energy
budget.
[3] Although a growing number of observations indicates
that the thermosphere-ionosphere (TI) system is continuously perturbed by GWs propagating from below [Forbes,
1
Department of Atmospheric, Oceanic and Space Sciences, University
of Michigan, Ann Arbor, Michigan, USA.
2
Max Planck Institute for Solar System Research, Katlenburg-Lindau,
Germany.
3
Atmospheric Physics Laboratory, Department of Physics and
Astronomy, University College London, London, UK.
Copyright 2009 by the American Geophysical Union.
0094-8276/09/2009GL038507
[4] We use the version of CMAT2 described in detail by
Yiğit et al. [2009]. The model domain extends from the
lower stratosphere (100 hPa, or 15 km) to the upper
thermosphere (typically 1.43 108 hPa, or 250 –
600 km) with 63 vertical levels (1/3 scale height discretization), and a 2° 18° latitude-longitude resolution. The
model parameterizations account for the absorption of solar
radiation by ozone in the Chappuis, Huggins, and Hartley
bands; by O2 in the Schumann-Runge bands, and for
heating due to the exothermic neutral chemistry. Thermospheric heating, photodissociation, and photoionization are
calculated for the absorption of solar X-rays, EUV, and UV
radiation between 1.8 –184 nm. Radiative cooling parameterizations include the 5.3 mm NO, 63 mm fine structure
atomic oxygen, local thermodynamic equilibrium (LTE) and
non-LTE 15.6 mm CO2, and 9.6 mm O3 radiative emissions.
The model incorporates appropriate representations of electric fields, auroral particle precipitation at high latitudes,
Joule heating, and ion drag. The morphology of the ionospheric electron density is taken from the Parameterized
Ionospheric Model (PIM) [Daniell et al., 1995]. In the
numerical experiments to be presented, we use prescribed
climatological distributions of chemical species and of the
Earth’s magnetic field. CMAT2 lacks a troposphere and, as
was described in the work by Yiğit et al. [2009], is forced at
the lower boundary by the NCEP reanalysis data and tidal
oscillations from the Global Scale Wave Model-02 [Hagan
and Forbes, 2003].
3. Results
[5] The utilized spectral GW scheme is essentially the
same as was described in detail by Yiğit et al. [2008, 2009].
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Figure 1. Zonal mean temperature averaged over the
period between 16 June and 6 July: (a) from the empirical
MSISE-90 model; (b) from EXP1 without GW heating/
cooling; (c) from EXP2 including the GW heating/cooling.
White contour lines mark temperature in 80 K intervals.
The amplitudes of wave momentum fluxes for harmonics
with the same horizontal wavelength (lh = 300 km) and
different phase velocities, ci, were kept constant at all times
and geographical locations throughout the simulations. The
morphology of this spectrum [Yiğit et al., 2009, Figure 1] is
in a very good agreement with the balloon measurements of
Hertzog et al. [2008, Figure 6]. Additionally, we assumed
that horizontal phase velocities of GW harmonics were
aligned along the direction of the local wind at the source
level, both up- and down the wind. As was absolutely
correctly noticed by S. Vadas, this source setup excluded
many of high-frequency and short-scale harmonics generated by convection. Vertical propagation of individual
harmonics with the horizontal phase speed ci and the
resulting momentum deposition rate (‘‘wave drag’’) ai were
calculated for all grid points. The total thermal effect of a
harmonic consists of the heating due to wave dissipation, Ei,
and the differential heating/cooling, Qi, associated with the
divergence of wave-induced heat flux, [Yiğit et al., 2008,
equation (6)]:
Ei ¼ c1
uÞ;
p ai ðci Qi ¼
H @
uÞ;
½rai ðci 2rR @z
ð1Þ
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where cp is the specific heat at constant pressure, H is the
density scale height, R is the gas constant, and r is the
background mass density. Unlike in the work by Yiğit et al.
[2009], contributions of all subgrid-scale harmonics were
not omitted here, but served as a forcing in the thermodynamic equation for resolved fields in CMAT2.
[6] We compare two model experiments: a) without
(EXP1) and b) with the included GW heating/cooling
(EXP2). In both cases, CMAT2 was run from the equinox
(21 March) till 6 July, and 4-hour outputs around the
solstice were analyzed. The geomagnetic and solar activity
were kept at constant low values (F10.7 = 80 1022 W
m2 Hz1; Kp = 2+) at all times to eliminate possible
uncertainties associated with their variations. The mean
effects of GW-induced heating rates on the simulated
temperature are illustrated in Figure 1. For that, the model
fields were averaged over the last 21 days of the simulations, that is between 16 June and 6 July. For comparison,
the temperature from the empirical MSISE-90 model was
processed in a similar manner, and is plotted in Figure 1a. It
is seen that the coldest (<140 K) temperature in the entire
model domain is found in the summer mesopause, while the
hottest (>900 K) is in the high-latitude summer upper
thermosphere. Figure 1b shows the zonal mean zonal
temperature from the run without GW heating/cooling
(EXP1). Although CMAT2 captures the mean temperature
structure reasonably well compared to MSISE-90, especially below the turbopause (<105 km), the simulated upper
thermospheric temperatures are noticeably higher. There are
many possible reasons for this overestimate, which are
related to uncertainties in radiation parameterizations, input
data, and the use of climatological distributions of radiatively active species. In particular, our own numerical
experiments demonstrated a high sensitivity to variations
of the atomic oxygen and of the adopted value of the
collisional quenching rate [Castle et al., 2006]. The temperature simulated in the run including the GW heating/
cooling (EXP2, Figure 1c) reveals much better agreement
with MSISE-90. It is seen that the overall thermal effect of
GWs above the tropopause is cooling. The warm temperature bias is reduced in EXP2 by more than 200 K over the
summer pole near the model top and by 100 to 170 K at
other latitudes in the thermosphere.
[7] Detailed illustrations of the GW heating and cooling
rates and their comparisons with other diabatic effects are
given in Figure 2. The irreversible heating Ei (Figure 2a) is
large in the high latitudes of both hemispheres and peaks at
90 to 100 K d1 near 200– 210 km. The secondary peak of
up to 10 K d1 is located in the tropics below 130– 140 km.
Note that the areas of enhanced GW heating do not
precisely coincide with those of wave drag. The latter is
distributed relatively uniformly in latitude [Yiğit et al., 2009,
Figure 3b] with maxima in midlatitudes. However, due to
strong filtering below, this drag in the high latitudes is created
by ‘‘surviving’’ harmonics with high phase speeds traveling
uj. This
against the mean wind, i.e. by those with high jci u)ai at high-latitudes,
explains large magnitudes of (ci and, therefore, strong GW heating and cooling. For example,
unlike with Ei, the drag has two thermospheric maxima in
each hemisphere: in the middle- and high-latitudes as well
as a weaker maximum over the equator below 130 km [Yiğit
et al., 2009, Figure 3b]. The role of the GW-induced heating
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Figure 2. 21-day averaged zonal mean heating/cooling rates simulated with CMAT2 (in K d1): (a) irreversible GW
heating (E); (b) total GW heating/cooling (E + Q); (c) Joule heating; (b) cooling due to molecular thermal conduction.
Shaded are the positive values.
is clearly seen when compared with the Joule heating. The
latter occurs due to collisions between charged and neutral
particles, and is an important diabatic heating mechanism in
the TI. The corresponding heating rates (Figure 2c) are up to
250 and 400 K d1 in the southern and northern hemispheres (SH and NH), respectively. Stronger heating in the
NH is largely due to higher ionization rates in the summer
hemisphere. Hence, in the high latitudes, the contribution of
GWs is between 20 and 40% of that by the Joule heating.
[8] However, the net effect of GWs is dominated by
cooling, especially in the upper thermosphere. As can be
seen from Figure 2b, the maxima of 180 and 150 K
d1 are formed at around 210 km in the high latitudes of the
SH and NH, respectively. There is also an area of marked
GW cooling of up to 60 K d1 in the midlatitudes of the
NH. Areas of the net GW heating (up to 60 K d1 in the
NH) lie just below. It follows from Figures 2a and 2b that
they are created by the differential heating/cooling Q, which
tends to redistribute the mean potential temperature vertically through GW-induced downward heat fluxes. In our
simulations, the differential cooling can reach up to 250
and 270 K d1 at 200 km in the high latitudes. The main
cooling mechanism in the upper thermosphere is the mo-
lecular thermal conduction. The corresponding rates (up to
1100 and 2300 K d1 in the SH and NH, respectively)
are plotted in Figure 2d. It is seen that GW cooling can
increase up to 10 and 20% of that by molecular heat
conduction.
[9] Having considered averaged thermal effects of GWs,
we now focus on their temporal and spatial variability. Our
simulations show that instantaneous values of the GWrelated heating and cooling rates can significantly exceed
the mean quantities discussed above. To illustrate the extent
of variations, we present few typical distributions from the
CMAT2 output on 22 June. The height-universal time (UT)
cross-sections of the temperature and total GW heating rates
Si (Ei + Qi) are plotted in Figures 3a and 3b for two fixed
geographical locations (75°S, 140°W) and (75°N, 140°W).
These points have been chosen because enhanced GW
activity occurs in the high latitudes. A strong dipole pattern
of heating below 190 km and cooling above is seen
between the local midnight and noon at 75°S. The heating
rates reach up to 500 K d1 at 170– 180 km and cooling
exceeds 1000 K d1 near 210 km. A reversed but
significantly weaker heating/cooling structure takes place
during the other half of the day. This day-night asymmetry
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Figure 3. The total GW heating/cooling rates (color-shaded) and temperature (white contour lines) simulated with
CMAT2 on 22 June: height-Universal time (UT) variations at (a) 75°S, 140°W and (b) 75°N, 140°W; geographical
distributions at (c) 0400 UT and (d) 1600 UT.
contributes to the daily and zonally averaged rates shown in
Figure 2d. The variations of heating rates are closely related
to the modulation of the GW drag by the diurnal tide, as was
discussed in section 9 of the work by Yiğit et al. [2009].
Two strong peaks of westerly momentum deposition at
10 UT and 16 UT (not shown here) take place at 200 –
210 km, just above the altitude that divides the regions of
GW heating and cooling. In the given longitude point of the
high-latitude NH, the total effect of GW heating is modulated by both diurnal and semi-diurnal tides, with maxima
of about 500 K d1 at 140 km.
[10] Snapshots of the GW-induced heating/cooling rates
at 210 km in Figures 3c and 3d illustrate an extent of the
spatial and temporal variability of the latter. The two
distributions, which are 12 hours apart, demonstrate that
most of the variations are associated with the sunsynchronous diurnal tides, especially in the mid- and high
latitudes in both hemispheres. Locally, the thermal effects of
GWs can significantly exceed the average values. For
example, an enhanced cooling of more than 3000 K d1
at 150°W in the SH appears particularly striking.
4. Summary and Conclusions
[11] Heating and cooling of the thermosphere by breaking
and/or dissipating small-scale internal gravity waves have
been studied for the first time using a comprehensive GCM
extending from the tropopause to the F2 region. A spectral
nonlinear GW parameterization suitable for these heights
[Yiğit et al., 2008] has been implemented in the CMAT2
GCM and estimates of GW-induced heating/cooling rates
for the June solstice have been obtained under low geomagnetic and solar activity conditions.
[12] The irreversible heating due to wave energy dissipation is strong (up to 100 K d1 in zonally and temporally
averaged sense) in the high latitudes of both hemispheres,
which constitutes between 20 and 40% of that by the Joule
heating. However, the net thermal effect of GWs above the
turbopause is dominated by cooling associated with the
divergence of the induced downward heat flux. The maxima
of 150 to 180 K d1 occur also in the high latitudes
around 210 km. When the total GW heating and cooling are
taken into account in the GCM, the simulated thermospheric
temperatures become colder: up to 200 K over the summer
pole, and up to 100 to 170 K at other latitudes near 210 km.
[13] Instantaneous values of GW heating and cooling
rates are highly variable, and can significantly exceed the
averaged quantities. In our simulations they can easily reach
up to 500 and 1100 K d1 and even more than 3000 K d1
locally in the F2 region. Most of variations and largest
heating/cooling rates take place in the high latitudes of both
hemispheres, and are strongly modulated by solar tides.
[14] It must be noted that GW effects in the upper
thermosphere, both dynamical [Yiğit et al., 2009] and
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thermal, are highly sensitive to the amount of momentum
prescribed to high phase speed GW harmonics in the source
spectrum. In our simulations, we used very moderate
constant values at the source level that are close to the
mean observed quantities [Hertzog et al., 2008] and are
typically employed in GCMs. However, convection can
generate fast GWs with amplitudes much higher than those
used here [Song and Chun, 2005]. Therefore, our results can
be viewed as very modest estimates, perhaps even underestimates, of GW-induced heating/cooling rates in the
thermosphere. Measurements of GW fluxes in the thermosphere and application of more sophisticated parameterizations of wave sources in the lower atmosphere can help
to quantify GW thermal effects further.
[15] The overall conclusion of this work is that heating
and cooling by dissipating GWs propagating from below
significantly contribute to the thermal balance of the thermosphere above the turbopause. They should not be
neglected in the thermosphere GCMs.
[16] Acknowledgments. This work was partially supported by the
German Science Foundation (DFG), project HA3261/4,5, and by AFOSR
grant FA9550-07-1-0434.
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A. S. Medvedev, Max Planck Institute for Solar System Research, MaxPlanck-Str. 2, D-37191 Katlenburg-Lindau, Germany. (medvedev@
mps.mpg.de)
E. Yiğit, Department of Atmosphere, Oceanic and Space Sciences,
University of Michigan, 1429 Space Research Building, 2455 Hayward
Street, Ann Arbor, MI 48109-2143, USA. ([email protected])
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